Skip to main content
SpringerLink
Log in

Coupled non-equilibrium fluctuations in a polymeric ternary mixture

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

We investigate by dynamic shadowgraphy the non-equilibrium fluctuations at the steady state of a thermodiffusion experiment in a polymeric ternary mixture of polystyrene-toluene-n-hexane. The structure function of the refractive index reveals the existence of quite different decay times, thus requiring the analysis of a wide range of correlation times. This is related to the simultaneous presence of three distinct decay modes corresponding to (from fastest to slowest) the relaxation of temperature fluctuations, of the concentration fluctuations of the mixed solvent, and of the concentration fluctuations of the polymer in the binary solvent. An investigation of the decay times at the corresponding diffusive regimes provides a measurement of the thermal diffusivity and the two eigenvalues of the mass diffusion matrix of the ternary mixture. Similar experiments were performed in the past but here, to suppress the confinement effect and obtain a more direct comparison with the theory, a thicker sample is studied. Moreover, also a faster camera is used allowing the experimental observation of faster modes, like the propagative ones. The experimental values of the decay times are eventually compared with those predicted by different available theories. Finally, we present a more complete theoretical model to describe the non-equilibrium fluctuations in the bulk of a ternary mixture at the steady state of a thermodiffusion experiment.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Montel, J. Bickert, A. Lagisquet, G. Galliero, J. Pet. Sci. Eng. 58, 391 (2007)

    Google Scholar 

  2. H. Guo, Q. Zhou, Z. Wang, Y. Huang, Int. J. Heat Mass Transfer 117, 966 (2018)

    Google Scholar 

  3. J.M. Ortiz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006)

    Google Scholar 

  4. F. Croccolo, J.M. Ortiz de Zárate, J.V. Sengers, Eur. Phys. J. E 39, 125 (2016)

    Google Scholar 

  5. A. Vailati, M. Giglio, Nature 390, 262 (1997)

    ADS  Google Scholar 

  6. F. Croccolo, H. Bataller, F. Scheffold, J. Chem. Phys. 137, 234202 (2012)

    ADS  Google Scholar 

  7. C. Giraudet, H. Bataller, F. Croccolo, Eur. Phys. J. E 37, 107 (2014)

    Google Scholar 

  8. C. Ludwig, Sitzungsber. Österr. Akad. Wiss., Math.-Nat. Kl. 20, 539 (1856)

    Google Scholar 

  9. C. Soret, Arch. Sci. Phys. Nat. Geneve 2, 48 (1879)

    Google Scholar 

  10. W. Köhler, K.I. Morozov, J. Non-Equilib. Thermodyn. 41, 151 (2016)

    ADS  Google Scholar 

  11. F. Croccolo, D. Brogioli, Appl. Opt. 50, 3419 (2011)

    ADS  Google Scholar 

  12. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Phys. Rev. E 76, 041112 (2007)

    ADS  Google Scholar 

  13. S.P. Trainoff, D.S. Cannell, Phys. Fluids 14, 1340 (2002)

    ADS  Google Scholar 

  14. H. Bataller, T. Triller, B. Pur, W. Köhler, J.M. Ortiz de Zárate, F. Croccolo, Eur. Phys. J. E 40, 35 (2017)

    Google Scholar 

  15. I. Lizarraga, C. Giraudet, F. Croccolo, M.M. Bou-Ali, H. Bataller, Micrograv. Sci. Technol. 28, 545 (2016)

    ADS  Google Scholar 

  16. J.K. Platten, M.M. Bou-Ali, P. Costeseque, J.F. Dutrieux, W. Köhler, C. Leppla, S. Wiegand, G. Wittko, Philos. Mag. 83, 1965 (2003)

    ADS  Google Scholar 

  17. H. Bataller, C. Giraudet, F. Croccolo, J.M. Ortiz de Zárate, Micrograv. Sci. Technol. 28, 611 (2016)

    ADS  Google Scholar 

  18. M.M. Bou-Ali, A. Ahadi, D. Alonso de Mezquia, Q. Galand, M. Gebhardt, O. Khlybov, W. Köhler, M. Larranaga, J.C. Legros, T. Lyubimova, A. Mialdun, I. Ryzhkov, M.Z. Saghir, V. Shevtsova, S. Van Vaerenbergh, Eur. Phys. J. E 38, 30 (2015)

    Google Scholar 

  19. A. Ahadi, S.V. Varenbergh, M.Z. Saghir, J. Chem. Phys. 138, 204201 (2013)

    ADS  Google Scholar 

  20. A. Mialdun, V. Shevtsova, J. Chem. Phys. 143, 224902 (2015)

    ADS  Google Scholar 

  21. A. Mialdun, I. Ryzhkov, O. Khlybov, T. Lyubimova, V. Shevtsova, J. Chem. Phys. 148, 044506 (2018)

    ADS  Google Scholar 

  22. T. Triller, H. Bataller, M.M. Bou-Ali, M. Braibanti, F. Croccolo, J.M. Ezquerro, Q. Galand, J. Gavaldà, E. Lapeira, A. Laverón-Simavilla, T. Lyubimova, A. Mialdun, J.M. Ortiz de Zárate, J. Rodríguez, X. Ruiz, I.I. Ryzhkov, V. Shevtsova, S.V. Vaerenbergh, W. Köhler, Micrograv. Sci. Technol. 30, 295 (2018)

    ADS  Google Scholar 

  23. A. Mialdun, H. Bataller, M.M. Bou-Ali, M. Braibanti, F. Croccolo, A. Errarte, J.M. Ezquerro, Y. Gaponenko, L. García-Fernández, J.J. Fernández, J. Rodríguez, V. Shevtsova, Eur. Phys. J. E 42, 87 (2019)

    Google Scholar 

  24. G. Galliero, H. Bataller, J.P. Bazile, J. Diaz, F. Croccolo, H. Hoang, R. Vermorel, P.A. Artola, B. Rousseau, V. Vesovic, M.M. Bou-Ali, J.M. Ortiz de Zárate, S. Xu, K. Zhang, F. Montel, A. Verga, O. Minster, npj Microgravity 3, 20 (2017)

    Google Scholar 

  25. J.C. Legros, S. Van Vaerenbergh, Y. Decroly, P. Colinet, F. Montel, Entropie 184/185, 38 (1994)

    Google Scholar 

  26. S. Van Vaerenbergh, S. Srinivasan, M.Z. Saghir, J. Chem. Phys. 131, 114505 (2009)

    ADS  Google Scholar 

  27. G. Galliero, H. Bataller, F. Croccolo, R. Vermorel, P.-A. Artola, B. Rousseau, V. Vesovic, M.M. Bou-Ali, J.M. Ortiz de Zárate, S. Xu, K. Zhang, F. Montel, Micrograv. Sci. Technol. 28, 79 (2015)

    ADS  Google Scholar 

  28. P. Baaske, H. Bataller, M. Braibanti, M. Carpineti, R. Cerbino, F. Croccolo, A. Donev, W. Köhler, J.M. Ortiz de Zárate, A. Vailati, Eur. Phys. J. E 39, 119 (2016)

    Google Scholar 

  29. M. Braibanti, P.-A. Artola, P. Baaske, H. Bataller, J.-P. Bazile, M.M. Bou-Ali, D.S. Cannell, M. Carpineti, R. Cerbino, F. Croccolo, J. Diaz, A. Donev, A. Errarte, J.M. Ezquerro, Q. Galand, G. Galliero, Y. Gaponenko, L. García-Fernández, J. Gavaldá, F. Giavazzi, M. Giglio, H. Hoang, W. Köhler, E. Lapeira, A. Laverón-Simavilla, I. Lizarraga, T. Lyubimova, S. Mazzoni, A. Mialdun, O. Minster, F. Montel, J.M. Ortiz de Zárate, J. Rodríguez, B. Rousseau, X. Ruiz, I.I. Ryzhkov, M. Schraml, V. Shevtsova, C.J. Takacs, T. Triller, S. Van Vaerenbergh, A. Vailati, A. Verga, R. Vermorel, V. Vesovic, V. Yasnou, S. Xu, D. Zapf, K. Zhang, Eur. Phys. J. E 42, 86 (2019)

    Google Scholar 

  30. P. Blanco, M.M. Bou-Ali, J.K. Platten, D.A. de Mezquia, J.A. Madariaga, C. Santamaria, J. Chem. Phys. 132, 114506 (2010)

    ADS  Google Scholar 

  31. A. Leahy-Dios, M.M. Bou-Ali, J.K. Platten, A. Firoozabadi, J. Chem. Phys. 122, 234502 (2005)

    ADS  Google Scholar 

  32. A. Königer, H. Wunderlich, W. Köhler, J. Chem. Phys. 132, 174506 (2010)

    ADS  Google Scholar 

  33. A. Ahadi, M. Ziad Saghir, Eur. Phys. J. E 38, 25 (2015)

    Google Scholar 

  34. A. Mialdun, J.C. Legros, V. Yasnou, V. Sechenyh, V. Shevtsova, Eur. Phys. J. E 38, 27 (2015)

    Google Scholar 

  35. M. Gebhardt, W. Kohler, Eur. Phys. J. E 38, 24 (2015)

    ADS  Google Scholar 

  36. Q. Galand, S. Van Vaerenbergh, Eur. Phys. J. E 38, 26 (2015)

    Google Scholar 

  37. O.A. Khlybov, Ryzhkov II, T.P. Lyubimova, Eur. Phys. J. E 38, 29 (2015)

    Google Scholar 

  38. M. Larranaga, M.M. Bou-Ali, D.A. de Mezquia, D.A. Rees, J.A. Madariaga, C. Santamaria, J.K. Platten, Eur. Phys. J. E 38, 28 (2015)

    Google Scholar 

  39. J.M. Ortiz de Zárate, C. Giraudet, H. Bataller, F. Croccolo, Eur. Phys. J. E 37, 77 (2014)

    Google Scholar 

  40. P. Martínez Pancorbo, J.M. Ortiz de Zárate, H. Bataller, F. Croccolo, Eur. Phys. J. E 40, 22 (2017)

    Google Scholar 

  41. C. Giraudet, H. Bataller, Y. Sun, A. Donev, J.M. Ortiz de Zárate, F. Croccolo, EPL 111, 60013 (2015)

    ADS  Google Scholar 

  42. C. Giraudet, H. Bataller, Y. Sun, A. Donev, J.M. Ortiz de Zárate, F. Croccolo, Eur. Phys. J. E 39, 120 (2016)

    Google Scholar 

  43. F. Croccolo, L. García-Fernández, H. Bataller, A. Vailati, J.M. Ortiz de Zárate, Phys. Rev. E 99, 012602 (2019)

    ADS  Google Scholar 

  44. D. Alonso de Mezquia, Z. Wang, E. Lapeira, M. Klein, S. Wiegand, M.M. Bou-Ali, Eur. Phys. J. E 37, 106 (2014)

    Google Scholar 

  45. J. Rauch, W. Köhler, J. Chem. Phys. 119, 11977 (2003)

    ADS  Google Scholar 

  46. K.J. Zhang, M.E. Briggs, R.W. Gammon, J.V. Sengers, J. Chem. Phys. 104, 6881 (1996)

    ADS  Google Scholar 

  47. D. Brogioli, A. Vailati, M. Giglio, Phys. Rev. E 61, 1 (2000)

    ADS  Google Scholar 

  48. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Appl. Opt. 45, 2166 (2006)

    ADS  Google Scholar 

  49. G. Cerchiari, F. Croccolo, F. Cardinaux, F. Scheffold, Rev. Sci. Instrum. 83, 106101 (2012)

    ADS  Google Scholar 

  50. L. Cipelletti, D.A. Weitz, Rev. Sci. Instrum. 70, 3214 (1999)

    ADS  Google Scholar 

  51. J.M. Ortiz de Zárate, Eur. Phys. J. E 42, 43 (2019)

    Google Scholar 

  52. J.M. Ortiz de Zárate, J.L. Hita, J.V. Sengers, C.R. Mec. 341, 399 (2013)

    ADS  Google Scholar 

  53. A. Bardow, Fluid Phase Equilib. 251, 121 (2007)

    Google Scholar 

  54. P.N. Segre, R. Schmitz, J.V. Sengers, Physica A 195, 31 (1993)

    ADS  Google Scholar 

  55. F. Croccolo, C. Giraudet, H. Bataller, R. Cerbino, A. Vailati, Micrograv. Sci. Technol. 28, 467 (2016)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire des Fluides Complexes et leurs Réservoirs - IPRA, UMR5150, E2S-Univ Pau & Pays Adour/CNRS/Total, 1 Allée du Parc Montaury, 64600, Anglet, France

    L. García-Fernández , P. Fruton, H. Bataller & F. Croccolo

  2. Centre National d’Études Spatiales (CNES), 2, Place Maurice Quentin, 75001, Paris, France

    L. García-Fernández

  3. Departamento de Estructura de la Materia, Física Térmica y Electrónica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Plaza de las Ciencias 1, 28040, Madrid, Spain

    J. M. Ortiz de Zárate

Authors
  1. L. García-Fernández
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Fruton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Bataller
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. M. Ortiz de Zárate
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. F. Croccolo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. García-Fernández .

Additional information

Publisher’s Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

García-Fernández , L., Fruton, P., Bataller, H. et al. Coupled non-equilibrium fluctuations in a polymeric ternary mixture. Eur. Phys. J. E 42, 124 (2019). https://doi.org/10.1140/epje/i2019-11889-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2019-11889-4

Keywords

Search

Navigation